Question: Factor completely. $49m^4+140m^2+100=$
Explanation: $\begin{aligned} &\phantom{=}49 m ^4 + 140 m ^2 + 100 \\\\ &= ({7 m ^2})^2 + 2({7 m ^2})({10 })+({10 })^2 \end{aligned}$ Using the square of a sum pattern: $\begin{aligned} &\phantom{=}({7 m ^2})^2 + 2({7 m ^2})({10 })+({10 })^2 \\\\ &=({7 m ^2} + {10 })^2 \end{aligned}$ In conclusion, $49 m ^4 + 140 m ^2 + 100 =(7 m ^2 + 10 )^2$ Remember that you can always check your factorization by expanding it.